1. Field of the Invention
Embodiments of the invention are most generally related to the field of optical phenomena in highly dispersive optical media, such phenomena being referred to herein as slow-light and fast-light optical phenomena. More particularly, embodiments of the invention are directed to fast- and slow-light-based optical interferometric, spectroscopic, and combined interferometric/spectroscopic apparatus and associated methods that provide improved measurement capabilities.
2. Background Discussion
The observation of optical interference phenomena can be traced back at least to the mid 17th century shortly before Huygens proposed his wave theory of light. Since then, many basic types of interferometers have been developed (e.g., two-beam, multiple-beam, grating-based, as well as others well known in the art) and their performance and scope of applications have continued to improve and grow, respectively.
Spectral sensitivity and spectral resolving power are two exemplary metrics of the performance of an interferometer, and are particularly significant performance metrics for a spectroscopic interferometer. Both spectral sensitivity and spectral resolving power are known to depend on the length, L, and the (phase) index of refraction, n, of the medium that a beam of light propagates through in an interferometer. These quantities affect the phase difference, Δφ, between a reference optical path and a measurement optical path having different L, n values. The phase difference affects the measurable intensity of the output signal(s) from the interferometer, which, in turn, directly impacts the measurement of various spectral parameters of the input optical field such as determined by spectral sensitivity and resolving power.
A more recent development in the field of optics involves the discovery and applications of what is known as slow-light and fast-light phenomena. The interested reader is directed to R. W. Boyd and D. J. Gauthier, in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), Vol. 43, pp. 497-530, the subject matter of which is incorporated herein by reference in its entirety to the fullest allowable extent.
Briefly, there is a well understood distinction between the phase velocity, vp, and the group velocity, vg, of a light field. The group velocity gives the velocity with which a pulse of light propagates through a material system. “Fast” or “slow” light depends on the value of the group velocity vg in comparison to the velocity of light c in a vacuum. “Slow” light refers to the situation vg<<c. “Fast” light refers to light traveling faster then the speed of light in a vacuum. This circumstance can occur either when vg>c or when vg is negative. A negative group velocity corresponds to the case when the peak of the pulse transmitted through an optical material emerges before the peak of the incident light field enters the medium.
For a monochromatic plane wave of angular frequency ω propagating through a medium of refractive index n, the wave can be described by the equationE(z,t)=Aei(kz−ωt)+C where k=nω/c. The phase velocity vp is defined as the velocity at which points of constant phase move through the medium. The phase of this wave is given byφ=kz−ωt, therefore, points of constant phase move a distance Δz in a time Δt, which are related bykΔz=ωΔt.Thus vp=Δz/Δt orvp=ω/k=c/n. 
One can next consider the propagation of a pulse through a material system. A pulse is necessarily composed of a spread of optical frequencies. At the peak of the pulse, the various frequency components will tend to add up in phase. If this pulse is to propagate without distortion, these components must add in phase for all values of the propagation distance z. To express this concept mathematically, one may write the phase of the wave asφ=(nωz/c)−ωt and require that there be no change in φ to first order in ω. That is, dφ/dω=0 or(dn/dω)(ωz/c)+(nz/c)−t=0,which can be written as z=vgt, where the group velocity is given byvg=c/(n+ωdn/dω)=dω/dk. The last equality in this equation results from the use of the relation k=nω/c. Alternatively, we can express this result in terms of a group refraction index ng defined byvg=c/ng withng=n+ωdn/dω. One can see that the group index differs from the phase index by a term that depends on the dispersion dn/dω of the refractive index.
Slow- and fast-light effects invariably make use of the rapid variation of refractive index that occurs in the vicinity of a material resonance. Slow-light can be achieved by making dn/dω large and positive (i.e., large normal dispersion), and fast-light occurs when the value of dn/dω is made large and negative (i.e., large anomalous dispersion).
Slow- and fast-light technology has recently attracted a great deal of interest, both in terms of fundamental and practical aspects. A potential application of slow light is in optical communications, where a tunable delay element can be used for all-optical buffering, data-synchronization, jitter correction, etc. One primary figure of merit of a slow-light delay element is the maximum fractional delay (also known as the delay-bandwidth product). This figure of merit is often limited by the maximum change in signal power level and the signal distortion that a practical system can tolerate.
In view of the foregoing concepts, information, and associated knowledge, the inventors have discovered new and useful apparatus and methods directed to spectral interferometers, spectrometers, and related apparatus, the spectral performance thereof, and the measurements made therewith. In particular, the inventors have recognized that numerous advantages would be associated with, e.g., a spectral interferometer and spectral interferometric methods having one or more of the following attributes: significantly increased spectral resolution for a conventionally-sized device, improved spectral sensitivity, at least conventional device performance in a significantly smaller-than-conventional device including chip-mounted devices (e.g., spectrometer-on-a-chip), improved reliability, reduced cost, more efficient operation, and more architecture adaptability and application suitability than provided by conventional devices.